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New results on fixed-time synchronization of impulsive neural networks via optimized fixed-time stability

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Abstract

In this paper, we investigated the fixed-time stability issue of a nonlinear impulsive dynamical system with general impulsive gains. First, we derived some novel fixed-time stability criteria by using the well-known comparison principle of impulsive systems and some suitable variable transformation method. Compared to finite-time stability, the fixed-time stability results provide a desired settling-time estimation which only depends on the system’s intrinsic parameters and has nothing to do with the initial value of the system. Then, based on the established stability results, the fixed-time synchronization of a type of neural networks with general impulsive effects is studied via using the Lyapunov function approach and some inequality techniques. Finally, we validated the effectiveness of developed theoretical results by providing three numerical examples. Compared with previous works, the impulsive gains in this paper not only can be stabilizing but also can be destabilizing, which provides wider application scope for the finite-time and fixed-time stability and synchronization studies of other impulse systems.

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Funding

This work was funded by the National Natural Science Foundation of China (Grant No. 62266042) and the Basic Research Program of Tianshan Talent Plan of Xinjiang, China (Grant No. 2022TSYCJU0005).

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, Xinjiang, People’s Republic of China

    Abdujelil Abdurahman, Rukeya Tohti & Cuicui Li

Authors
  1. Abdujelil Abdurahman
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  2. Rukeya Tohti
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  3. Cuicui Li
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Contributions

AA: Writing, visualization, and Funding acquisition. RT: Review and Editing. CL: Writing original draft and Methodology.

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Correspondence to Abdujelil Abdurahman.

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Abdurahman, A., Tohti, R. & Li, C. New results on fixed-time synchronization of impulsive neural networks via optimized fixed-time stability. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02072-w

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  • DOI: https://doi.org/10.1007/s12190-024-02072-w

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